an:06137924
Zbl 1258.05038
Omidi, G. R.; Shahsiah, M.
On the choice number of packings
EN
J. Comb. Des. 20, No. 11-12, 504-507 (2012).
00310870
2012
j
05C15 05C65 05C70
hypergraph; \(t\)-design; choice number; packing
Summary: In this note, we show that for positive integers \(s\) and \(k\), there is a function \(D(s,k)\) such that every \(t\)-\((v,k,\lambda)\) packing with at least \(D(s,k)\lambda ^{k-t}s^{t-2} v \binom{v-2}{t-2}/\binom{k-2}{t-2}\) edges, \(2 \leq t \leq k-1\), has choice number greater than \(s\).
Consequently, for integers \(s\), \(k\), \(t\), and \(\lambda \) there is a \(v_{0}(s,k,t,\lambda)\) such that every \(t\)-\((v,k,\lambda)\) design with \(v > v_{0}(s,k,t,\lambda)\) has choice number greater than \(s\).